1. Field of the Invention
The invention relates to a variable gain amplifier, and more particularly, to a variable gain amplifier having a gain liner-in-decibel with respect to controlling voltages.
2. Description of the Prior Art
Recently wireless communication systems have been developing very fast. As a result, many kinds of high bandwidth high sensitivity transceivers are proposed. Variable gain amplifiers are often used in this kind of transceiver to broaden the processing range of the system. A variable gain amplifier that has a gain liner in decibel (dB) with respect to controlling voltage(s) has relatively broader gain range.
Please refer to FIG. 1 where a circuit of a conventional variable gain amplifier is illustrated. The variable gain amplifier shown in FIG. 1 is a differential amplifier. The voltage gain Av of the whole circuit can be determined from the half circuit of the differential amplifier. Disregarding the phase, the voltage gain Av of this variable gain amplifier will be:
                    Av        =                                            Vout              ′                                      Vin              ′                                =                      K                          1              +                              exp                ⁡                                  (                                      Vy                    Vt                                    )                                                                                        (        1        )            where K is substantially a constant value.
From equation (1) it can be seen that the denominator of the voltage gain Av comprises not only a simple exponential function but also a constant term 1. Consequently, the voltage gain Av does not have a perfectly exponential relationship with respect to the controlling voltage Vy.
Please refer to FIG. 2. FIG. 2 is a graph for showing the relation between the voltage gain Av and the controlling voltage Vy of FIG. 1. Note that when Vy<Vt, the voltage gain Av will not change exponentially with respect to the change in the controlling voltage Vy. The smaller the controlling voltage Vy is, the less the voltage gain Av will change with respect to the change in the controlling voltage Vy. This phenomenon where the voltage gain Av does not have perfect exponential relationship with the controlling voltage Vy is caused by the constant term 1.